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Zbl 1123.35342
Gerdjikov, Vladimir; Valchev, Tihomir
Breather solutions of $N$-wave equations. (English)
[A] Mladenov, Iva\"ilo (ed.) et al., Proceedings of the 8th international conference on geometry, integrability and quantization, Sts. Constantine and Elena, Bulgaria, June 9--14, 2006. Sofia: Bulgarian Academy of Sciences. 184-200 (2007). ISBN 978-954-8495-37-0/pbk

Summary: We consider $N$-wave type equations related to symplectic and orthogonal algebras. We obtain their soliton solutions in the case when two different $\bbfZ_2$ reductions (or equivalently one $\bbfZ_2\times \bbfZ_2$-reduction) are imposed. For that purpose we apply a particular case of an auto-Bäcklund transformation -- the Zakharov-Shabat dressing method. The corresponding dressing factor is consistent with the $\bbfZ_2\times\bbfZ_2$-reduction. These soliton solutions represent $N$-wave breather-like solitons. The discrete eigenvalues of the Lax operators connected with these solitons form ``quadruplets" of points which are symmetrically situated with respect to the coordinate axes.

MSC 2000:: *35Q51 Solitons
37K35 Lie-Bäcklund and other transformations
58J72 Correspondences and other transformation methods

Keywords: auto-Bäcklund transformation; dressing method; breather-like solitons; discrete eigenvalues; Lax operators

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